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Lixin Xu

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astro-ph.CO gr-qc hep-th astro-ph hep-ph Computer Vision Graphics Machine Learning math-ph math.MP

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preprint2026arXiv

Equivariant Cohomology, BRST Quantization, and Analytic Localization: A Unified Framework

This paper provides a detailed exposition of the two main models for equivariant cohomology -- the Cartan and Weil models -- and their explicit isomorphism via the Kalkman (Mathai--Quillen) transformation. We then connect this framework to the BRST quantization of gauge theories, showing how the BRST complex can be identified with the Cartan model. Viewing both the Kalkman transformation and Witten's Morse-theoretic deformation as gauge-fixing procedures leads naturally to the \emph{equivariant Witten deformation}. This combined perspective yields a transparent analytic proof of the Atiyah--Bott--Berline--Vergne (ABBV) localization formula for integrals of equivariantly closed forms.The theory is richly illustrated with computations on $\mathbb{CP}^1$ and $\mathbb{CP}^n$, supplemented by explicit coordinate calculations.

preprint2026arXiv

R-DMesh: Video-Guided 3D Animation via Rectified Dynamic Mesh Flow

Video-guided 3D animation holds immense potential for content creation, offering intuitive and precise control over dynamic assets. However, practical deployment faces a critical yet frequently overlooked hurdle: the pose misalignment dilemma. In real-world scenarios, the initial pose of a user-provided static mesh rarely aligns with the starting frame of a reference video. Naively forcing a mesh to follow a mismatched trajectory inevitably leads to severe geometric distortion or animation failure. To address this, we present Rectified Dynamic Mesh (R-DMesh), a unified framework designed to generate high-fidelity 4D meshes that are ``rectified'' to align with video context. Unlike standard motion transfer approaches, our method introduces a novel VAE that explicitly disentangles the input into a conditional base mesh, relative motion trajectories, and a crucial rectification jump offset. This offset is learned to automatically transform the arbitrary pose of the input mesh to match the video's initial state before animation begins. We process these components via a Triflow Attention mechanism, which leverages vertex-wise geometric features to modulate the three orthogonal flows, ensuring physical consistency and local rigidity during the rectification and animation process. For generation, we employ a Rectified Flow-based Diffusion Transformer conditioned on pre-trained video latents, effectively transferring rich spatio-temporal priors to the 3D domain. To support this task, we construct Video-RDMesh, a large-scale dataset of over 500k dynamic mesh sequences specifically curated to simulate pose misalignment. Extensive experiments demonstrate that R-DMesh not only solves the alignment problem but also enables robust downstream applications, including pose retargeting and holistic 4D generation.

preprint2022arXiv

Can phantom transition at $z\sim 1$ restore the Cosmic concordance?

The tension among inferences of Hubble constant ($H_0$) is found in a large array of datasets combinations. Modification to the late expansion history is the most direct solution to this discrepancy. In this work, we examine the viability of restoring the cosmological concordance with a novel version of transitional dark energy (TDE). The main anchors for the cosmic distance scale: cosmic microwave background (CMB) radiation, baryon acoustic oscillation (BAO), and Type Ia supernova (SNe Ia) calibrated by Cepheids form a "impossible trinity", i.e., it's plausible to reconcile with any two of the three but unlikely to accommodate them all. Particularly, the tension between BAO and the calibrated SNe Ia can not be reconciled within the scenarios of late dark energy. Nevertheless, our analysis suggests that the TDE model can reconcile with CMB and SNe Ia calibrated by its absolute magnitude ($M_{\rm{B}}$) when the equation of state (EoS) of DE transits around $z\sim1$. Meanwhile, we see a positive sign that the EoS transits with the inclusion of a local prior on $M_{\rm{B}}$, whereas the opposite is true without the $M_{\rm{B}}$ prior.

preprint2022arXiv

Comparing the scalar-field dark energy models with recent observations

We investigate the general properties of a class of scalar-field dark energy models (i.e., $ϕ$CDM models) which behave like cosmological trackers at early times. Particularly, we choose three $ϕ$CDM models with typical potentials, i.e., $V(ϕ)\propto ϕ^{-α}$ (inverse power-law (IPL) model), $V(ϕ)\propto \coth^αϕ$ (L-model) and $V(ϕ)\propto \cosh(αϕ)$ (Oscillatory tracker model), where the latter two models are based on the $α$-attractors originated from the study of inflation. These models, which reduce to the $Λ$CDM model with $α\to 0$, are studied and compared with the recent observations, including the Pantheon sample of type Ia supernovae (SNe Ia), baryon acoustic oscillations (BAO) measurements extracted from 6dFGS, BOSS and eBOSS, as well as the temperature and polarization anisotropy power spectra data of cosmic microwave background radiation (CMB) from Planck 2018 results. The observational constraints from the combining sample (SNe Ia + BAO + CMB) indicate that none of the three $ϕ$CDM models exclude the $Λ$CDM model at $68.3\%$ confidence level. We find that the CMB anisotropy data have obvious advantages in constraining the dark energy models compared with other cosmological probes, which is particularly evident in the L-model. Furthermore, we apply the Bayesian evidence to compare the $ϕ$CDM models and the $Λ$CDM model with the analysis of the combining sample. The concordance $Λ$CDM model is still the most supported one. In addition, among the three $ϕ$CDM models, the IPL model is the most competitive one, while the L-model/Oscillatory tacker model is moderately/strongly disfavored.

preprint2022arXiv

Limit on the dark matter mass from its interaction with photons

In this work, we explore the phenomenology of generalized dark matter (GDM) which interacts with photons ($γ$). We assume that DM establishes elastic scattering with $γ$ when it has already become nonrelativistic, otherwise the abundance of DM today is disfavored by current observations. Within this scenario, the equation of state (EoS) of DM is determined by its mass ($m_χ$) and the DM-$γ$ scattering cross-section. The distinctive imprints of a nonzero EoS of DM on CMB angular power spectrum allow us to set a lower limit on $m_χ$ with Planck 2018 data alone, i.e., $m_χ > 8.7$ keV at $95\%$ C.L. In the study of cosmic concordance problems, we find that the GDM scenario preserves the sound horizon ($r_s(z_*)$) predicted in the fiducial $Λ$CDM model, and thus does not solve the $H_0$ tension. When performing the joint analysis of Planck+LSS datasets, the best-fit $S_8= 0.785\pm 0.017$ closely matches the given $S_8$ prior. This suggests that the GDM scenario can be counted as a viable candidate to restore the $S_8$ ($σ_{8}$) tension.

preprint2021arXiv

Testing the effect of $H_0$ on $fσ_8$ tension using a Gaussian Process method

Using the $fσ_8(z)$ redshift space distortion (RSD) data, the $σ_8^0-Ω_m^0$ tension is studied utilizing a parameterization of growth rate $f(z) = Ω_m(z)^γ$. Here, $f(z)$ is derived from the expansion history $H(z)$ which is reconstructed from the observational Hubble data applying the Gaussian Process method. It is found that different priors of $H_0$ have great influences on the evolution curve of $H(z)$ and the constraint of $σ_8^0-Ω_m^0$. When using a larger $H_0$ prior, the low redshifts $H(z)$ deviate significantly from that of the $Λ$CDM model, which indicates that a dark energy model different from the cosmological constant can help to relax the $H_0$ tension problem. The tension between our best-fit values of $σ_8^0-Ω_m^0$ and that of the \textit{Planck} 2018 $Λ$CDM (PLA) will disappear (less than $1σ$) when taking a prior for $H_0$ obtained from PLA. Moreover, the tension exceeds $2σ$ level when applying the prior $H_0 = 73.52 \pm 1.62$ km/s/Mpc resulted from the Hubble Space Telescope photometry. By comparing the $S_8 -Ω_m^0$ planes of our method with the results from KV450+DES-Y1, we find that using our method and applying the RSD data may be helpful to break the parameter degeneracies.

preprint2019arXiv

General Cosmography Model with Spatial Curvature

The cosmographic approach is adopted to determine the spatial curvature (i.e., $Ω_K$) combining the latest released cosmic chronometers data (CC), the Pantheon sample of type Ia supernovae observations, and the baryon acoustic oscillation measurements. We use the expanded transverse comoving distance $D_M(z)$ as a basic function for deriving $H(z)$ and the other cosmic distances. In this scenario, $Ω_K$ can be constrained only by CC data. To overcome the convergence issues at high-redshift domains, two methods are applied: the Padé approximants and the Taylor series in terms of the new redshift $y=z/(1+z)$. Adopting the Bayesian evidence, we find that there is positive evidence for the Padé approximant up to order ($2,2$) and weak evidence for the Taylor series up to 3-rd order against $Λ\text{CDM}+Ω_K$ model. The constraint results show that a closed universe is preferred by the present observations under all the approximants used in this study. And the tension level of the Hubble constant $H_0$ is less than $2σ$ significance between different approximants and the local distance ladder determination. For each assumed approximant, $H_0$ is anti-correlated with $Ω_K$ and the sound horizon at the end of the radiation drag epoch, which indicates that the $H_0$ tension problem can be slightly relaxed by introducing $Ω_K$ or any new physics which can reduce the sound horizon in the early universe.

preprint2016arXiv

Detecting the Neutrinos Mass Hierarchy from Cosmological Data

We propose a new parameterization to measure the neutrino mass hierarchy, namely $Δ=(m_3-m_1)/(m_1+m_3)$ which is dimensionless and varies in the range $[-1,1]$. Taking into account the results of neutrino oscillation experiments, $Δ$ is the unique parameter for determining all the masses of neutrinos, and a positive (negative) sign of $Δ$ denotes the normal (inverted) mass hierarchy. Adopting the currently available cosmic observations, we find that the normal mass hierarchy is slightly favored, and the mass of lightest neutrino is less than $0.030$ eV for the normal mass hierarchy and $0.024$ eV for the inverted mass hierarchy at $95\%$ confidence level.

preprint2016arXiv

Distinguish three time-dependent dark energy models using statefinder pairs with error bars and Bayesian evidence

In this work, two completely different approaches, statefinder with error bars and Bayesian evidence, are used to distinguish and judge three time-dependent dark energy models. The parameters constrain for the three dark energy models are given using the current cosmic observational data sets : $Planck$ 2015, SNIa, BAO and OHD. Using the statefinder pairs with error bars, we find that the error region of the dark energy model, whose equation of state parameter is given by $w(a) = w_0+w_3\frac{1-a}{a^2+(1-a)^2}$, is relativity compact than the other two models during the all the evolving history. Meanwhile, the Bayesian evidence also provide that this model is significantly better than the other two models and the other two models are inconclusive. Then, there are reasons for believing that this model is a preferential candidate in dark energy investigation rather than the other two.

preprint2016arXiv

New constraints on cosmic polarization rotation from the ACTPol cosmic microwave background B-Mode polarization observation and the BICEP2 constraint update

Recently ACTPol has measured the cosmic microwave background (CMB) B-mode and E-mode polarizations and obtained TE, EE, BB, TB and EB power spectra in the multipole range 225-8725. In our previous paper (Ap. J. 792 (2014) 35 [Paper I]), we have analyzed jointly the results of three experiments on the CMB B-mode polarization -- SPTpol, POLARBEAR and BICEP2 to include in the model, in addition to the gravitational lensing and the inflationary gravitational waves components, also the fluctuation effects induced by the cosmic polarization rotation (CPR), if it exists within the upper limits at the time. In this paper, we fit both the mean CPR angle <α> and its fluctuation <δα2> from the new ACTPol data, and update our fitting of CPR fluctuations using BICEP2 data taking the new Planck dust measurement results into consideration. We follow the method of Paper I. The mean CPR angle is constrained from the EB correlation power spectra to |<α>| < 14 mrad (0.8°) and the fluctuation (rms) is constrained from the BB correlation power spectra to <δα2>1/2 < 29.3 mrad (1.68°). Assuming that the polarization angle of Tau A does not change from 89.2 to 146 GHz, the ACTPol data give <α> = 1.0 {\pm} 0.63°. These results suggest that the inclusion of the present ACTPol data is consistent with no CPR detection. With the new Planck dust measurement, we update our fits of the BICEP2 CPR fluctuation constraint to be 32.8 mrad (1.88°). The joint ACTpol-BICEP2-POLARBEAR CPR fluctuation constraint is 23.7 mrad (1.36°).

preprint2016arXiv

Probing the Neutrino Mass through the Cross Correlation between the Rees-Sciama Effect and Weak Lensing

Cosmology plays a fundamental role to determine the neutrino mass, therefore also to determine its mass hierarchy, since the massive neutrino contributes to the total matter density in the Universe at the background and perturbation levels, once it becomes non-relativistic. After the non-relativistic transition the fluctuations are smashed out at the scales $k\gg k_{fs}$. Therefore, the missing fluctuation in the total matter is imprinted on the large scale structure, say the suppression of the matter power spectrum $ΔP/P\approx -8f_ν$ at the scales $k\gg k_{fs}$. In this paper, instead of considering the linear perturbation theory, which is well understood in the presence of neutrino, we propose to use the cross correlation between the Rees-Sciama effect and weak lensing to probe the neutrino mass. At the small scales, the density contrast grows faster than the background scale factor $δ\sim a$, that makes a sign flipping on $Φ' \propto \mathcal{H}δd\ln (δ/a)/d\ln a$, which happens only in the non-linear regime. We show that the flipping scale in the cross power spectrum between the Rees-Sciama effect and weak lensing depends on the neutrino mass by assuming the shallow and deep weak lensing surveys. Our analysis shows that the Deep survey has larger signal-to-noise ratio $S/N\sim 160$. Finally, we use the Fisher information matrix to forecast constraint on the neutrino mass.

preprint2016arXiv

Thermodynamics of Apparent Horizon and Friedmann Equations in Big Bounce Universe

In this paper, we study a big bounce universe typified by a non-singular big bounce, as opposed to a singular big bang. This cosmological model can describe radiation dominated early universe and matter dominated late universe in FRW model. The connections between thermodynamics and gravity are observed here. In the early stage of both cold and hot universes, we find there is only one geometry containing a 4D de Sitter universe with a general state parameter. We also find the form of the apparent horizon in the early universe strongly depends on the extra dimension, which suggests that the influence of the extra dimension could in principle be found in the early universe. Moreover, we show that in the late stages of both cold and hot universes, the moment when the apparent horizon begins to bounce keeps essentially in step with the behavior of the cosmological scalar factor.

preprint2015arXiv

Constraint on $f(R)$ Gravity through the Redshift Space Distortion

In this paper, a specific family of $f(R)$ models that can produce the $Λ$CDM background expansion history is constrained by using the currently available geometric and dynamic probes. The scale dependence of the growth rate $f(z,k)$ in this specific family of $f(R)$ model is shown. Therefore to eliminate the scale dependence of $fσ_8(z)$ in theory, which usually is defined as the product of $f(z,k)$ and $σ_8(z)$, we define $fσ_8(z)=dσ_8(z)/d\ln a$ which is obviously scale independent and reproduces the conventional definition in the standard $Λ$CDM cosmology. In doing so, under the assumption that future probes having the same best fit values as the current ten data points of $fσ_8(z)$, even having $20\%$ error bars enlarged, we find a preliminary constraint $f_{R0}=-2.58_{-0.58}^{+2.14}\times 10^{-6}$ in $1σ$ regions. This indicates the great potential that redshift space distortions have in constraining modified gravity theories. We also discuss the nonlinear matter power spectrum based on different halo fit models.

preprint2015arXiv

Constraints on the dark matter equation of state with redshift-space distortion

In this paper, we study a model which is composed by the cosmological constant and dark matter with nonzero equation of state parameter, which could be called as $Λ$wDM. In the synchronous gauge, we obtain the perturbation equations of dark matter, and deduce the evolution equations of growth factor about the dark matter and baryons. Based on the Markov Chain Monte Carlo method, we constrain this model by the recently available cosmic observations which include cosmic microwave background radiation, baryon acoustic oscillation, type Ia supernovae, and $fσ_8(z)$ data points from redshift-space distortion. The results present a tighter constraint on the model than the case without $fσ_8(z)$ data. In 3$σ$ regions, we find the dark matter equation of state parameter $w_{dm}$=$0.000111_{- 0.000701-0.00137-0.00180}^{+0.000688+0.00136+0.00181}$. After an extra model parameter $w_{dm}$ is considered, the difference between the minimum values of $χ^2$ of our model and standard model is $Δχ^2_{min}=0.598$. Although the currently available cosmic observations mildly favor the nonzero dark matter equation of state parameter, no significant deviation from the $Λ$CDM model is found in 1$σ$ region.

preprint2015arXiv

Exploring a new interaction between dark matter and dark energy using the growth rate of structure

We present a phenomenological interaction with a scale factor power law form which leads to the appearance of two kinds of perturbed terms, a scale factor spatial variation along with perturbed Hubble expansion rate. We study both the background and the perturbation evolution within the parametrized post-Friedmann scheme, obtaining that the exchange of energy-momentum can flow from dark energy to dark matter in order to keep dark energy and dark matter densities well defined at all times. We combine several measures of the cosmic microwave background (WMAP9+Planck) data, baryon acoustic oscillation measurements, redshift-space distortion data, JLA sample of supernovae, and Hubble constant for constraining the coupling constant and the exponent provided both parametrized the interaction itself. The joint analysis of ${\rm Planck+WMAP9+BAO}$ ${\rm +RSD+JLA+HST}$ data seems to favor large coupling constant, $ξ_c = 0.34403427_{- 0.18907353}^{+ 0.14430125}$ at 1 $σ$ level, and prefers a power law interaction with a negative exponent, thus $β= -0.50863232_{- 0.40923857}^{+ 0.48424166}$ at 1 $σ$ level. The CMB temperature power spectrum indicates that a large coupling constant produces a shift of the acoustic peaks and affects their amplitudes at lower multipoles. In addition, a larger $β$ exponent generates a shift of the acoustic peaks, pointing a clear deviation with respect to the concordance model. The matter power spectrum are sensitive to the variation of the coupling constant and the $β$ exponent. In this context, the interaction alters the scale of matter and radiation equality and pushes it away from the present era, which in turn generates a shift of the turnover point toward to smaller scale.

preprint2015arXiv

FRCAMB: An $f(R)$ Code for Anisotropies in the Microwave Background

An $f(R)$ gravity model is proposed to realize a late time accelerated expansion of our Universe. To test the viability of an $f(R)$ gravity model through cosmic observations, the background evolution and the Einstein-Boltzmann equation should be solved for studying the effects on the cosmic microwave background power spectrum and on the matter power spectrum. In the market, we already have the modified versions of {\bf CAMB} code, for instance {\bf EFTCAMB} and {\bf MGCAMB}. However, in these publicly available Einstein-Boltzmann codes, a specific background cosmology, for example the $Λ$CDM or $w$CDM, is assumed. This assumption would be non-proper for a specific $f(R)$ model where the background evolution may be different from a $Λ$CDM cosmology. Therefore the main task for this paper is to present a code to calculate the anisotropies in the microwave background for any $f(R)$ gravity model based on {\bf CAMB} code, i.e. {\bf FRCAMB}, where the background and perturbation evolutions are included consistently. As results, one can treat {\bf FRCAMB} as a blackbox to output the CMB power spectrum and matter power spectrum, once an $f(R)$ function, its first two derivative with respect to $R$, i.e. $f_R\equiv df/dR$, $f_{RR}\equiv d^2f/dR^2$ and the reasonable values of the model parameters are inputted properly. As by-products, one can also output the effective equation of state of $f(R)$ model, the evolution of the dimensionless energy densities and other interesting cosmological quantities.

preprint2015arXiv

Galaxy clustering, CMB and supernova data constraints on $ϕ$CDM model with massive neutrinos

We investigate a scalar field dark energy model (i.e., $ϕ$CDM model) with massive neutrinos, where the scalar field possesses an inverse power-law potential, i.e., $V(ϕ)\propto ϕ^{-α}$ ($α>0$). We find that the sum of neutrino masses $Σm_ν$ has significant impacts on the CMB temperature power spectrum and on the matter power spectrum. In addition, the parameter $α$ also has slight impacts on the spectra. A joint sample, including CMB data from Planck 2013 and WMAP9, galaxy clustering data from WiggleZ and BOSS DR11, and JLA compilation of Type Ia supernova observations, is adopted to confine the parameters. Within the context of the $ϕ$CDM model under consideration, the joint sample determines the cosmological parameters to high precision. It turns out that $α<4.995$ at 95% CL for the $ϕ$CDM model. And yet, the $Λ$CDM scenario corresponding to $α= 0$ is not ruled out at 95% CL. Moreover, we get $Σm_ν< 0.262$ eV at 95% CL for the $ϕ$CDM model, while the corresponding one for the $Λ$CDM model is $Σm_ν < 0.293$ eV. The allowed scale of $Σm_ν$ in the $ϕ$CDM model is a bit smaller than that in the $Λ$CDM model. It is consistent with the qualitative analysis, which reveals that the increases of $α$ and $Σm_ν$ both can result in the suppression of the matter power spectrum. As a consequence, when $α$ is larger, in order to avoid suppressing the matter power spectrum too much, the value of $Σm_ν$ should be smaller.

preprint2015arXiv

Gravitational Waves: A Test for Modified Gravity

In a modified gravity theory, the propagation equation of gravitational waves will be presented in a non-standard way. Therefore this tenor mode perturbation of time-space, as a complement to the scalar mode perturbation, provides a unique character distinguishing modified gravity from general relativity. To avoid the model-dependent issue, in this paper, we propose a parametrised modification to the propagation of gravitational waves. We show the effects on the angular power spectrum of cosmic microwave background radiation due to the parametrised modification and its degeneracy to the tensor mode power spectrum index $n_t$ and its running $α_t$. At last, we report the current status on the detection of modified gravity through the currently available cosmic observations. Our results show no significant deviation to general relativity.

preprint2015arXiv

Reduced modified Chaplygin gas cosmology

In this paper, we study cosmologies containing the reduced modified Chaplygin gas (RMCG) fluid which is reduced from the modified Chaplygin gas $p=Aρ-Bρ^{-α}$ for the value of $α=-1/2$. In this special case, dark cosmological models can be realized for different values of model parameter $A$. We investigate the viabilities of these dark cosmological models by discussing the evolutions of cosmological quantities and using the currently available cosmic observations. It is shown that the special RMCG model ($A=0$ or $A=1$) which unifies the dark matter and dark energy should be abandoned. For $A=1/3$, RMCG which unifies the dark energy and dark radiation is the favorite model according to the objective Akaike information criteria. In the case of $A<0$, RMCG can achieve the features of the dynamical quintessence and phantom models, where the evolution of the universe is not sensitive to the variation of model parameters.

preprint2014arXiv

Confronting Dark Energy Anisotropic Stress

We use the currently available cosmic observations to probe and constrain an imperfect dark energy fluid which is characterized by a constant equation of state $w$ and a constant speed of viscosity $c^2_{vis}$. The model parameter space was scanned by using Markov chain Monte Carlo method. The results show that the speed of viscosity $c^2_{vis}$ was not well constrained when currently available date sets, which include the cosmic microwave background radiation from {\it Planck}2013, type Ia supernovae and baryon acoustic oscillations, are used. But the cosmic data sets favor phantom dark energy with a negative speed of viscosity $c^2_{vis}$ slightly.

preprint2014arXiv

Confronting DGP Braneworld Gravity with Cosmic Observations after Planck Data

The normal branch of Dvali-Gabadadze-Porrati braneworld gravity with brane tension is confronted by the currently available cosmic observations from the geometrical and dynamical perspectives. On the geometrical side, the type Ia supernova as standard candle, the baryon acoustic oscillation as standard ruler and the cosmic microwave background measurement from the first released 15.5 months data were used to fix the background evolutions. On the dynamical side, the redshift space distortion data will be used to determine the evolution of the matter perturbation. Through a Markov chain Monte Carlo analysis, we found the dimensionless crossover scale $Ω_{r_c}=1/(4H^2_0r^2_{c})=0.00183_{-0.00183}^{+0.000338}$ in a spatially flat normal branch of Dvali-Gabadadze-Porrati braneworld. This result suggests that the crossover scale $r_c$ should be around $12H^{-1}_0$ which is consistent with the previous result $r_c>3H^{-1}_0$ and greater. It also implies that the five-dimensional gravity effect is weak to be observed in $H^{-1}_0$ scale.

preprint2014arXiv

Constraints on a decomposed dark fluid with constant adiabatic sound speed by jointing the geometry test and growth rate after Planck data

In this paper, a unified dark fluid with constant adiabatic sound speed is decomposed into cold dark matter interacting with vacuum energy. Based on Markov chain Monte Carlo method, we constrain this model by jointing the geometry and dynamical measurement. The geometry test includes cosmic microwave background radiation from \textit{Planck}, baryon acoustic oscillation, and type Ia supernovae; the dynamic measurement is $fσ_8(z)$ data points which is obtained from the growth rate via redshift-space distortion, and $σ_8(z)$ is the root-mean-square amplitude of the density contrast $δ$ at the comoving $8h^{-1}$ Mpc scale. The jointed constraint shows that $α$ = $ 0.000662_{- 0.000662}^{+ 0.000173}$ and $σ_8$ = $ 0.824_{- 0.0166}^{+ 0.0128}$. The CMB and matter power spectra are both similar for the case of $α=$ mean value and that of $α=0$. However, the evolutionary curves of $fσ_8(z)$ are different. This means that, to some extent, the data points of the growth rate could break the degeneracy of the dark energy models.

preprint2014arXiv

Cosmological constraints on interacting dark energy with redshift-space distortion after Planck data

The interacting dark energy model could propose a effective way to avoid the coincidence problem. In this paper, dark energy is taken as a fluid with a constant equation of state parameter $w_x$. In a general gauge, we could obtain two sets of different perturbation equations when the momentum transfer potential is vanished in the rest frame of dark matter or dark energy. There are many kinds of interacting forms from the phenomenological considerations, here, we choose $Q=3Hξ_xρ_x$ which owns the stable perturbations in most cases. Then, according to the Markov Chain Monte Carlo method, we constrain the model by currently available cosmic observations which include cosmic microwave background radiation, baryon acoustic oscillation, type Ia supernovae, and $fσ_8(z)$ data points from redshift-space distortion. Jointing the geometry tests with the large scale structure information, the results show a tighter constraint on the interacting model than the case without $fσ_8(z)$ data. We find the interaction rate in 3$σ$ regions: $ξ_x=0.00372_{-0.00372- 0.00372-0.00372}^{+0.000768+0.00655+0.0102}$. It means that the recently cosmic observations favor a small interaction rate between the dark sectors, at the same time, the measurement of redshift-space distortion could rule out a large interaction rate in the 1$σ$ region.

preprint2014arXiv

Cosmology with hybrid expansion law: scalar field reconstruction of cosmic history and observational constraints

In this paper, we consider a simple form of expansion history of Universe referred to as the hybrid expansion law - a product of power-law and exponential type of functions. The ansatz by construction mimics the power-law and de Sitter cosmologies as special cases but also provides an elegant description of the transition from deceleration to cosmic acceleration. We point out the Brans-Dicke realization of the cosmic history under consideration. We construct potentials for quintessence, phantom and tachyon fields, which can give rise to the hybrid expansion law in general relativity. We investigate observational constraints on the model with hybrid expansion law applied to late time acceleration as well as to early universe a la nucleosynthesis.

preprint2014arXiv

Coupled dark energy with perturbed Hubble expansion rate

The coupling between dark sectors provides a possible approach to mitigate the coincidence problem of cosmological standard model. In this paper, dark energy is treated as a fluid with a constant equation of state, whose coupling with dark matter is proportional the Hubble parameter and energy density of dark energy, that is, $\bar{Q}=3ξ_x\bar{H}\barρ_x$. Particularly, we consider the Hubble expansion rate to be perturbed in the perturbation evolutions of dark sectors. Using jointing data sets which include cosmic microwave background radiation, baryon acoustic oscillation, type Ia supernovae, and redshift-space distortions, we perform a full Monte Carlo Markov Chain likelihood analysis for the coupled model. The results show that the mean value with errors of interaction rate is: $ξ_x=0.00305_{-0.00305-0.00305-0.00305}^{+0.000645+0.00511+0.00854}$ for $Q^μ_A\parallel u^μ_c$; $ξ_x=0.00317_{-0.00317-0.00317-0.00317}^{+0.000628+0.00547+0.00929}$ for $Q^μ_A\parallel u^μ_x$, which means that the recently cosmic observations favored small interaction rate which is up to the order of $10^{-3}$. Moreover, in contrast to the coupled model with unperturbed expansion rate, we find perturbed Hubble expansion rate could bring about negligible impact on the model parameter space.

preprint2014arXiv

Detecting Primordial Gravitational Waves Signal from BICEP2 and {\it Planck} HFI $353$GHz Dust Polarization

The dust polarization is parameterized as a power law form of the multipole $l$: $D^{XX}_{l}=A^{XX}l(l+1)l^{α_{XX}}/(2π)$ ($XX$ denotes $BB$ or $EE$), where $A^{XX}$ is its amplitude with the ratio $A^{BB}/A^{EE}=0.52\pm 0.02$ and $α_{BB,EE}=-2.42\pm 0.02$. Extrapolating to $150$GHz from $353$GHz yields a value of $D^{BB}_{l=80}=(1.32\pm 0.29)\times 10^{-2}μK^2$ (and an additional uncertainty $(+0.28,-0.24)\times 10^{-2}μK^2$) over the range $40<l<120$. Based on these data, we report the tensor-to-scalar ratio $r=A_{t}/A_{s}$ defined at $k_0=0.05 \text{Mpc} ^{-1}$ by joining the BICEP2+{\it Planck}2013+WMAP9+BAO+HST and {\it Planck} HFI $353$GHz dust polarization and its implication to the detection of the primordial gravitational waves. Considering the $Λ$CDM+$r$ model, we found $r<0.108$ at $95\%$ confidence level with $σ_{stat}=0.29$ and $r<0.129$ at $95\%$ confidence level with $σ_{stat+extr}=0.29+0.28$. The results imply no significant evidence for the primordial gravitational waves in $1σ$ regions. However the post probability distribution of $r$ peaks at a small positive value. And $r$ moves to larger positive values when the extrapolation error bars are included. This might imply a very weak signal of the primordial gravitational waves. It also implies the crucial fact in calibrating the amplitude of the dust polarizations in detecting the primordial gravitational waves in the future. When the running of the scalar spectral tilt is included, we found $r<0.079$ at $95\%$ confidence level with $σ_{stat}=0.29$ and $r=0.091_{-0.069}^{+0.042}$ at $95\%$ confidence level with $σ_{stat+extr}=0.29+0.28$. The later one implies the detection of the primordial gravitational waves in $1σ$ regions at the cost of decreasing the value of $D^{BB}_{l=80}$ to $0.67_{-0.25}^{+0.25}$.

preprint2014arXiv

Interacting parametrized post-Friedmann method

We apply the interacting parametrized post-Friedmann (IPPF) method to a coupled dark energy model where the interaction is proportional to dark matter density at background level. In doing so, we perform a Markov Chain Monte-Carlo analysis which combines several cosmological probes including the cosmic microwave background (WMAP9+Planck) data, baryon acoustic oscillation (BAO) measurements, JLA sample of supernovae, Hubble constant (HST), and redshift-space distortion (RSD) measurements through the ${\rm f}σ_{8}{\rm (z)}$ data points. The joint observational analysis of ${\rm Planck+WP+JLA+BAO+HST+RSD}$ data leads to a coupling parameter, $ξ_{c}=0.00140_{-0.00080}^{+0.00079}$ at $1σ$ level for vanishing momentum transfer potential; this value is reduced a when the momentum transfer potential is switched on, giving $ξ_{c}=0.00136_{-0.00073}^{+0.00080}$ at $1σ$ level. The CMB power spectrum shows up a correlation between the coupling parameter $ξ_{c}$ and the position of acoustic peaks or their amplitudes. The first peak's height increases when $ξ_{c}$ takes larger values and its position is shifted. We also obtain the matter power spectrum may be affected by the strength of interaction coupling over scales bigger that $10^{-2} {\rm h~ Mpc^{-1}}$, reducing its amplitude in relation to the vanilla model.

preprint2014arXiv

Observational constraints on variable equation of state parameters of dark matter and dark energy after Planck

In this paper, we study a cosmological model in general relativity within the framework of spatially flat Friedmann-Robertson-Walker space-time filled with ordinary matter (baryonic), radiation, dark matter and dark energy, where the latter two components are described by Chevallier-Polarski-Linder equation of state parameters. We utilize the observational data sets from SNLS3, BAO and Planck+WMAP9+WiggleZ measurements of matter power spectrum to constrain the model parameters. We find that the current observational data offer tight constraints on the equation of state parameter of dark matter. We consider the perturbations and study the behavior of dark matter by observing its effects on CMB and matter power spectra. We find that the current observational data favor the cold dark matter scenario with the cosmological constant type dark energy at the present epoch.

preprint2014arXiv

Post-$Planck$ constraints on interacting vacuum energy

We present improved constraints on an interacting vacuum model using updated astronomical observations including the first data release from Planck. We consider a model with one dimensionless parameter, $α$, describing the interaction between dark matter and vacuum energy (with fixed equation of state $w=-1$). The background dynamics correspond to a generalised Chaplygin gas cosmology, but the perturbations have a zero sound speed. The tension between the value of the Hubble constant, $H_0$, determined by Planck data plus WMAP polarisation (Planck+WP) and that determined by the Hubble Space Telescope (HST) can be alleviated by energy transfer from dark matter to vacuum ($α>0$). A positive $α$ increases the allowed values of $H_0$ due to parameter degeneracy within the model using only CMB data. Combining with additional datasets of including supernova type Ia (SN Ia) and baryon acoustic oscillation (BAO), we can significantly tighten the bounds on $α$. Redshift-space distortions (RSD), which constrain the linear growth of structure, provide the tightest constraints on vacuum interaction when combined with Planck+WP, and prefer energy transfer from vacuum to dark matter ($α<0$) which suppresses the growth of structure. Using the combined datasets of Planck+WP+Union2.1+BAO+RSD, we obtain the constraint on $α$ to be $-0.083<α<-0.006$ (95% C.L.), allowing low $H_0$ consistent with the measurement from 6dF Galaxy survey. This interacting vacuum model can alleviate the tension between RSD and Planck+WP in the $Λ$CDM model for $α<0$, or between HST measurements of $H_0$ and Planck+WP for $α>0$, but not both at the same time.

preprint2014arXiv

Probing kinematics and fate of the Universe with linearly time-varying deceleration parameter

The parametrizations $q=q_0+q_1 z$ and $q=q_0+q_1 (1-a/a_0)$ (Chevallier-Polarski-Linder parametrization) of deceleration parameter, which are linear in cosmic redshift $z$ and scale factor $a$, have been frequently utilized in the literature to study kinematics of Universe. In this paper, we follow a strategy that leads to these two well known parametrizations of deceleration parameter as well as an additional new parametrization $q=q_0+q_1(1-t/t_0)$, which is linear in cosmic time $t$. We study the features of this linearly time-varying deceleration parameter in contrast with the other two linear parametrizations. We investigate in detail the kinematics of the Universe by confronting the three models with the latest observational data. We further study the dynamics of the Universe by considering the linearly time-varying deceleration parameter model in comparison with the standard $Λ$CDM model. We also discuss future of the Universe in the context of the models under consideration.

preprint2014arXiv

Pursuing the Amplitude of Tensor Mode Power Spectrum in Light of BICEP2

In this brief report, we try to constrain general parameterized forms of scalar and tensor mode power spectra, $P_{s}(k)\equiv A_s(k/k_0)^{n_s-1+\frac{1}{2}α_s\ln(k/k_0)}$ and $P_{t}(k)\equiv A_t(k/k_0)^{n_t+\frac{1}{2}α_t\ln(k/k_0)}$ by the recently released BICEP2 data set plus {\it Planck} 2013, WMAP9 and BAO. We loosen the inflationary consistence relations, and take $A_s$, $n_s$, $A_t$ and $n_t$ as free model parameters, via the Markov chain Monte Carlo method, the interested model parameter space was investigated, we obtained marginalized $68\%$ limits on the interested parameters are: $n_s=0.96339_{-0.00554}^{+0.00560}$, $n_t=1.70490_{-0.56979}^{+0.56104}$, ${\rm{ln}}(10^{10} A_s)=3.08682_{-0.02614}^{+0.02353}$ and ${\rm{ln}}(10^{10} A_t)=3.98376_{-0.54885}^{+0.86045}$. The ratio of the amplitude at the scale $k=0.002 \text{Mpc} ^{-1}$ is $r=0.01655_{-0.01655}^{+0.00011}$ which is consistent with the {\it Planck} 2013 result.

preprint2014arXiv

Reconciling the Tension Between Planck and BICEP2 Through Early Dark Energy

We show the possibility that the observational results of the primordial gravitational waves from Planck and BICEP2 for the tensor-to-scalar ratio $r$ can be reconciled when an early dark energy was included. This early dark energy behaves like a radiation component at very early epoch. This is equivalent to induce additional number of effective neutrino species: $ΔN_{eff}=[\frac{7}{8}(\frac{4}{11})^{4/3}]^{-1}ρ_{de}(a)/ρ_γ(a)$, where $ρ_γ(a)$ is the photon energy density and the numerical factors arise from converting to effective neutrino species. And $ρ_{de}(a)$ is the energy density of early dark energy. Combining the Planck temperature data, the WMAP9 polarization data, and the baryon acoustic oscillation data with and without BICEP2 data, we find that in this early dark energy model the tension between the observations from Planck and BICEP2 was relived at $2σ$ regions. But it cannot be removed completely due to the small ratio of early dark energy constrained by the other cosmic observations. As a byproduct, the tension between observed values of Hubble parameter from Planck and the direct measurement of the Hubble constant was removed in this early dark energy model.

preprint2014arXiv

Spherical Collapse for Viscous Generalized Chaplygin Gas Model

The nonlinear collapse for viscous generalized Chaplygin gas Model (VGCG) was analyzed in the framework of spherical top-hat collapse. As the VGCG and baryons are essential to form the large scale structure, we focused on their nonlinear collapse in this paper. We discussed the influence of model parameters $α$ and $ζ_{0}$ on the spherical collapse by varying their values and compare with $ΛCDM$. The results show that, for the VGCG model, smaller $ζ_{0}$ and larger $α$ make the structure formation earlier and faster, and the collapse curves of VGCG model is almost distinguished with the $ΛCDM$ model when the model parameter $α$ is less than $10^{-2}$.

preprint2014arXiv

Spherical top-hat Collapse of a Viscous Unified Dark Fluid

In this paper, we test the spherical collapse of a viscous unified dark fluid (VUDF) which has constant adiabatic sound speed and show the nonlinear collapse for VUDF, baryons, and dark matter which are important to form the large scale structure of our Universe. By varying the values of model parameters $α$ and $ζ_{0}$, we discuss their effects on the nonlinear collapse of the VUDF model, and compare its result to $ΛCDM$ model. The analyzed results show that, within the spherical top-hat collapse framework, larger values of $α$ and smaller values of $ζ_{0}$ make the structure formation earlier and faster, and the other collapse curves are almost distinguished with the curve of $Λ CDM$ model if the bulk viscosity coefficient $ζ_{0}$ is less than $10^{-3}$.

preprint2014arXiv

Testing coupled dark energy with large scale structure observation

The coupling between the dark components provides a new approach to mitigate the coincidence problem of cosmological standard model. In this paper, dark energy is treated as a fluid with a constant equation of state, whose coupling with dark matter is $\bar{Q}=3Hξ_x\barρ_x$. In the frame of dark energy, we derive the evolution equations for the density and velocity perturbations. According to the Markov Chain Monte Carlo method, we constrain the model by currently available cosmic observations which include cosmic microwave background radiation, baryon acoustic oscillation, type Ia supernovae, and $fσ_8(z)$ data points from redshift-space distortion. The results show the interaction rate in 3$σ$ regions: $ξ_x=0.00328_{-0.00328-0.00328-0.00328}^{+0.000736+0.00549+0.00816}$, which means that the recently cosmic observations favor a small interaction rate which is up to the order of $10^{-2}$, meanwhile, the measurement of redshift-space distortion could rule out the large interaction rate in the 1$σ$ region.

preprint2014arXiv

Viscous Generalized Chaplygin Gas as a Unified Dark Fluid: Including Perturbation of Bulk Viscosity

In this paper, we continue our previous work of studying viscous generalized Chaplygin gas (VGCG) as a unified dark fluid but including the bulk viscosity perturbation. By using the currently available cosmic observational data from SNLS3, BAO, HST and recently released Planck, we gain the constraint on bulk viscosity coefficient: $ζ_0=0.0000138_{- 0.0000105- 0.0000138- 0.0000138}^{+ 0.00000614+ 0.0000145+ 0.0000212}$ in $1, 2, 3σ$ regions respectively via Markov Chain Monte Carlo method. The result shows that when considering perturbation of bulk viscosity, the currently cosmic observations favor a smaller bulk viscosity coefficient.

preprint2013arXiv

Constraints on Dark Matter annihilation and Its Equation of State after Planck Data

In this paper, the annihilation of dark matter $f_dε_0$ with nonzero equation of state $w_{dm}$ was studied by using the currently available cosmic observations which include the geometric and dynamic measurements. The constrained results show they are anti-correlated and are $w_{dm}=0.000390_{-0.000753}^{+0.000754}$ and $f_dε_0=1.172_{-1.172}^{+0.243}$ respectively in $1σ$ regions. With the including of possible annihilation of dark matter, no significant deviation from $Λ$CDM model was found in the $1σ$ region.

preprint2013arXiv

Constraints on the Holographic Dark Energy Model from Type Ia Supernovae, WMAP7, Baryon Acoustic Oscillation and Redshift-Space Distortion

In this paper, we use the joint measurement of geometry and growth rate from matter density perturbations to constrain the holographic dark energy model. The geometry measurement includes type Ia supernovae (SN Ia) Union2.1, full information of cosmic microwave background (CMB) from WMAP-7yr and baryon acoustic oscillation (BAO). For the growth rate of matter density perturbations, the results $f(z)σ_8(z)$ measured from the redshift-space distortion (RSD) in the galaxy power spectrum are employed. Via the Markov Chain Monte Carlo method, we try to constrain the model parameters space. The jointed constraint shows that $c=0.750_{- 0.0999- 0.173- 0.226}^{+ 0.0976+ 0.215+ 0.319}$ and $σ_8=0.763_{- 0.0465- 0.0826- 0.108}^{+ 0.0477+ 0.0910+ 0.120}$ with $1,2,3σ$ regions. After marginalizing the other irrelevant model parameters, we show the evolution of the equation of state of HDE with respect to the redshift $z$. Though the current cosmic data points favor a phantom like HDE Universe for the mean values of the model parameters in the future, it can behave like quintessence in $3σ$ regions.

preprint2013arXiv

Cosmological constraints on a decomposed Chaplygin gas

Any unified dark matter cosmology can be decomposed into dark matter interacting with vacuum energy, without introducing any additional degrees of freedom. We present observational constraints on an interacting vacuum plus dark energy corresponding to a generalised Chaplygin gas cosmology. We consider two distinct models for the interaction leading to either a barotropic equation of state or dark matter that follows geodesics, corresponding to a rest-frame sound speed equal to the adiabatic sound speed or zero sound speed, respectively. For the barotropic model, the most stringent constraint on $α$ comes from the combination of CMB+SNIa+LSS(m) gives $α<5.66\times10^{-6}$ at the 95% confidence level, which indicates that the barotropic model must be extremely close to the $Λ$CDM cosmology. For the case where the dark matter follows geodesics, perturbations have zero sound speed, and CMB+SNIa+gISW then gives the much weaker constraint $-0.15<α<0.26$ at the 95% confidence level.

preprint2013arXiv

Growth Index after the Planck Results

The growth index $γ_L$ was proposed to investigate the possible deviation from the standard $Λ$CDM model and Einstein's gravity theory in a dynamical perspective. Recently, thanks to the measurement of the cosmic growth rate via the redshift-space distortion, one can understand the evolution of density contrast through $fσ_8(z)$, where $f(z)=d\ln δ/d \ln a$ is the growth rate of matter and $σ_8(z)$ is the rms amplitude of the density contrast $δ$ at the comoving $8h^{-1}$ Mpc scale. In this paper, we use the redshift space distortion data points to study the growth index on the bases of Einstein's gravity theory and a modified gravity theory under the assumption of $f=Ω_m(a)^{γ_L}$. The cosmic background evolution is fixed by the cosmic observations from the type Ia supernovae SNLS3, cosmic microwave background radiation data from {\it Planck} and baryon acoustic oscillations. Via the Markov Chain Monte Carlo method, we found the $γ_L$ values for Einstein's gravity with a cosmological constant, $w=constant$ dark energy and a modified gravity theory in the $1,2,3σ$ regions respectively: $0.675_{-0.0662-0.120-0.155}^{+0.0611+0.129+0.178}$, $0.745_{-0.0819-0.146-0.190}^{+0.0755+0.157+0.205}$ and $0.555_{-0.0167-0.0373-0.0516}^{+0.0193+0.0335+0.0436}$. In the Einstein's gravity theory, the values of growth index $γ_L$ show almost $2σ$ deviation from the theoretical prediction 6/11 for the $Λ$CDM model. However in the modified gravity framework, a deviation from the Einstein's relativity is not detected in $1σ$ region. That implies that the currently available cosmic observations don't expect an alternative modified gravity theory beyond the $Λ$CDM model under Einstein's gravity, but that the simple assumption of $f=Ω_m^{γ_L}$ should be improved.

preprint2013arXiv

Spherical Collapse of a Unified Dark Fluid with Constant Adiabatic Sound Speed

In this paper, we test the spherical collapse of a unified dark fluid (UDF) which has constant adiabatic sound speed. By choosing the different values of model parameters $B_s$ and $α$, we show the nonlinear collapse for UDF and baryons which are considered for their formation of the large scale structure of our Universe. The analyzed results show that larger values of $α$ and $B_s$ make the structure formation faster and earlier.

preprint2013arXiv

Strong Gravitational Lensing and Its Cosmic Constraints

In this paper, we propose a new method to use the strong lensing data sets to constrain a cosmological model. By taking the ratio $\mathcal{D}^{obs}_{ij}=θ_{\mathrm{E_{\mathrm{i}}}}σ_{\mathrm{0_{\mathrm{j}}}}^2/θ_{\mathrm{E_{\mathrm{j}}}}σ_{\mathrm{0_{\mathrm{i}}}}^2$ as cosmic observations, one can {\it completely} eliminate the uncertainty caused by the relation $σ_{\mathrm{SIS}}=f_{\mathrm{E}}σ_0$ which characterizes the relation between the stellar velocity dispersion $σ_0$ and the velocity dispersion $σ_{SIS}$. Via our method, a relative tight constraint to the cosmological model space can be obtained, for the spatially flat $Λ$CDM model as an example $Ω_m=0.143_{- 0.143-0.143-0.143}^{+ 0.000769+0.143+0.489}$ in $3σ$ regions. And by using this method, one can also probe the nature of dark energy and the spatial curvature of our Universe.

preprint2013arXiv

Unified Dark Fluid with Constant Adiabatic Sound Speed: Including Entropic Perturbations

In this paper, we continue to study a unified dark fluid model with a constant adiabatic sound speed but with the entropic perturbations. When the entropic perturbations are included, an effective sound speed, which reduces to the adiabatic sound speed when the entropic perturbations are zero, has to be specified as an additional free model parameter. Due to the relations between the adiabatic sound speed and equations of state (EoS) $c^2_{s,ad}(a)=w(a)-d\ln(1+w(a))/3 d\ln a$, the equation of state can be determined up to an integration constant in principle when an adiabatic sound speed is given. Then there are two degrees of freedom to describe the linear perturbations for a fluid. Its micro-scale properties are characterized by its EoS or adiabatic sound speed and an effective sound speed. We take the effective sound speed and adiabatic sound speed as free model parameters and then use the currently available cosmic observational data sets, which include type Ia supernova Union 2.1, baryon acoustic oscillation and WMAP 7-year data of cosmic background radiation, to constrain the possible entropic perturbations and the adiabatic sound speed via the Markov Chain Monte Carlo method. The results show that the cosmic observations favor a small effective sound speed $c^2_{s,eff}=0.00155_{- 0.00155}^{+ 0.000319}$ in $1σ$ region.

preprint2013arXiv

Unified dark fluid with fast transition: including entropic perturbations

In this paper, we investigate a unified dark fluid model with fast transition and entropic perturbations. An effective sound speed is designated as an additional free model parameter when the entropic perturbations are included, and if the entropic perturbations are zero, the effective sound speed will decrease to the adiabatic sound speed. In order to analyze the viability of the unified model, we calculate the squared Jeans wave number with the entropic perturbations. Furthermore, by using the Markov Chain Monte Carlo method, we perform a global fitting for the unified dark fluid model from the type Ia supernova Union 2.1, baryon acoustic oscillation and the full information of cosmic microwave background measurement given by the WMAP 7-yr data points. The constrained results favor a small effective sound speed. Compared to the $Λ$CDM, it is found that the cosmic observations do not favor the phenomenon of fast transition for the unified dark fluid model.

preprint2012arXiv

A New Unified Dark Fluid Model and Its Cosmic Constraint

In this paper, we propose a new unified dark fluid (UDF) model with equation of state (EoS) $w(a)=-α/(βa^{-n}+1)$, which includes the generalized Chaplygin gas model (gGg) as its special case, where $α$, $β$ and $n$ are three positive numbers. It is clear that this model reduces to the gCg model with EoS $w(a)=-B_s/(B_s+(1-B_s)a^{-3(1+α)})$, when $α=1$, $β=(1-B_s)/B_s$ and $n=3(1+α)$. By combination the cold dark matter and the cosmological constant, one can coin a EoS of unified dark fluid in the form of $w(a)=-1/(1+(1-Ω_Λ)a^{-3}/Ω_Λ)$. With this observations, our proposed EoS provides a possible deviation from $Λ$CDM model when the model parameters $α$ and $n$ deviate from 1 and 3 respectively. By using the currently available cosmic observations from type Ia supernovae (SN Ia) Union2.1, baryon acoustic oscillation (BAO) and cosmic microwave background radiation (CMB), we test the viability of this model and detect the possible devotion from the $Λ$CDM model. The results show that the new UDF model fits the cosmic observation as well as that of the $Λ$CDM model and no deviation is found from the $Λ$CDM model in $3σ$ confidence level. However, our new UDF model can give a non-zero sound speed, as a contrast, which is zero for the $Λ$CDM model. We expect the large structure formation information can distinct the new UDF model from the $Λ$CDM model.

preprint2012arXiv

Constraints to Holographic Dark Energy Model via Type Ia Supernovae, Baryon Acoustic Oscillation and WMAP

In this paper, the holographic dark energy (HDE) model, where the future event horizon is taken as an IR cut-off, is confronted by using currently available cosmic observational data sets which include type Ia supernovae, baryon acoustic oscillation and cosmic microwave background radiation from full information of WMAP-7yr. Via the Markov Chain Monte Carlo method, we obtain the values of model parameter $c= 0.696_{- 0.0737- 0.132- 0.190}^{+ 0.0736+ 0.159+ 0.264}$ with $1,2,3σ$ regions. Therefore one can conclude that at lest $3σ$ level the future Universe will be dominated by phantom like dark energy. It is not consistent with positive energy condition, however this condition must be satisfied to derive the holographic bound. It implies that the current cosmic observational data points disfavor the HDE model.

preprint2012arXiv

Cosmological Model-independent Gamma-ray Bursts Calibration and its Cosmological Constraint to Dark Energy

As so far, the redshift of Gamma-ray bursts (GRBs) can extend to $z\sim 8$ which makes it as a complementary probe of dark energy to supernova Ia (SN Ia). However, the calibration of GRBs is still a big challenge when they are used to constrain cosmological models. Though, the absolute magnitude of GRBs is still unknown, the slopes of GRBs correlations can be used as a useful constraint to dark energy in a completely cosmological model independent way. In this paper, we follow Wang's model-independent distance measurement method and calculate their values by using 109 GRBs events via the so-called Amati relation. Then, we use the obtained model-independent distances to constrain $Λ$CDM model as an example.

preprint2012arXiv

Modified Chaplygin Gas as a Unified Dark Matter and Dark Energy Model and Cosmic Constraints

A modified Chaplygin gas model (MCG), $ρ_{MCG}/ρ_{MCG0}=[B_{s}+(1-B_{s})a^{-3(1+B)(1+α)}]^{1/(1+α)}$, as a unified dark matter model and dark energy model is constrained by using current available cosmic observational data points which include type Ia supernovae, baryon acoustic oscillation and the seventh year full WMAP data points. As a contrast to the consideration in the literatures, we {\it do not} separate the MCG into two components, i.e. dark mater and dark energy component, but we take it as a whole energy component-a unified dark sector. By using Markov Chain Monte Carlo method, a tight constraint is obtained: $α= 0.000727_{- 0.00140- 0.00234}^{+ 0.00142+ 0.00391}$, $B=0.000777_{- 0.000302- 0.000697}^{+ 0.000201+ 0.000915}$ and $B_s= 0.782_{- 0.0162- 0.0329}^{+ 0.0163+ 0.0307}$ .}

preprint2012arXiv

Revisiting Cardassian Model and Cosmic Constraint

In this paper, we revisit the Cardassian model in which the radiation energy component is included. It is important for early epoch when the radiation cannot be neglected because the equation of state (EoS) of the effective dark energy becomes time variable. Therefore, it is not equivalent to the quintessence model with a constant EoS anymore. This situation was almost overlooked in the literature. By using the recent released Union2 557 of type Ia supernovae (SN Ia), the baryon acoustic oscillation (BAO) from Sloan Digital Sky Survey and the WiggleZ data points, the full information of cosmic microwave background (CMB) measurement given by the seven-year Wilkinson Microwave Anisotropy Probe observation, we constrain the Cardassian model via the Markov Chain Monte Carlo (MCMC) method. A tight constraint is obtained: $n= -0.0479_{- 0.0732- 0.148}^{+ 0.0730+ 0.142}$ in $1,2σ$ regions. The deviation of Cardassian model from quintessence model is shown in CMB anisotropic power spectra at high l's parts due to the evolution of EoS. But it is about the order of 0.1% which cannot be discriminated by current data sets. The Cardassian model is consistent with current cosmic observational data sets.

preprint2012arXiv

Revisiting Generalized Chaplygin Gas as a Unified Dark Matter and Dark Energy Model

In this paper, we revisit generalized Chaplygin gas (GCG) model as a unified dark matter and dark energy model. The energy density of GCG model is given as $ρ_{GCG}/ρ_{GCG0}=[B_{s}+(1-B_{s})a^{-3(1+α)}]^{1/(1+α)}$, where $α$ and $B_s$ are two model parameters which will be constrained by type Ia supernova as standard candles, baryon acoustic oscillation as standard rulers and the seventh year full WMAP data points. In this paper, we will not separate GCG into dark matter and dark energy parts any more as adopted in the literatures. By using Markov Chain Monte Carlo method, we find the result: $α=0.00126_{- 0.00126- 0.00126}^{+ 0.000970+ 0.00268}$ and $B_s= 0.775_{- 0.0161- 0.0338}^{+ 0.0161+ 0.0307}$.

preprint2012arXiv

Unified Dark Fluid with Constant Adiabatic Sound Speed and Cosmic Constraints

As is known above 90% of the energy content in Universe is made of unknown dark component. Usually this dark fluid is separated into two parts: dark matter and dark energy. However, it may be a mixture of these two energy components, or just one exotic unknown fluid. This property is dubbed as dark degeneracy. With this motivation, in this paper, a unified dark fluid having constant adiabatic sound speed $c_s^2=α$, which is in the range $[0,1]$, is studied. At first, via the energy conservation equation, its energy density, $ρ_d/ρ_{d0}=(1-B_s)+B_s a^{-3(1+α)}$ where $B_s$ is related to integration constant from energy conservation equation as another model parameter, is presented. Then by using Markov Chain Monte Carlo method with currently available cosmic observational data sets which include type Ia supernova Union 2, baryon acoustic oscillation and WMAP 7-year data of cosmic background radiation, we show that small values of $α$ are favored in this unified dark fluid model. Furthermore, we show that smaller values of $α<10^{-5}$ are required to match matter (baryon) power spectrum from SDSS DR7.

preprint2011arXiv

$Λ(t)$CDM Model as a Unified Origin of Holographic and Agegraphic Dark Energy Models

Motivated by the fact that any nonzero $Λ$ can introduce a length scale or a time scale into Einstein's theory, $r_Λ=ct_Λ=\sqrt{3/|Λ|}$. Conversely, any cosmological length scale or time scale can introduce a $Λ(t)$, $Λ(t)=3/r^2_Λ(t)=3/(c^2t^2_Λ(t))$. In this letter, we investigate the time varying $Λ(t)$ corresponding to the length scales, including the Hubble horizon, the particle horizon and the future event horizon, and the time scales, including the age of the universe and the conformal time. It is found out that, in this scenario, the $Λ(t)$CDM model can be taken as the unified origin of the holographic and agegraphic dark energy models with interaction between the matter and the dark energy, where the interacting term is determined by $Q=-\dotρ_Λ$. We place observational constraints on the $Λ(t)$CDM models originating from different cosmological length scales and time scales with the recently compiled "Union2 compilation" which consists of 557 Type Ia supernovae (SNIa) covering a redshift range $0.015\leq z \leq 1.4$. In conclusion, an accelerating expansion universe can be derived in the cases taking the Hubble horizon, the future event horizon, the age of the universe and the conformal time as the length scale or the time scale.

preprint2011arXiv

CMB Temperature and Matter Power Spectrum in a Decay Vacuum Dark Energy Model

In this paper, a decay vacuum model $\barρ_Λ=3σM_p^2H_0 H$ is revisited by detailed analysis of background evolution and perturbation equations. We show the imprints on CMB temperature and matter power spectrum from the effective coupling terms between dark sectors by comparing to the standard cosmological constant model and observational data points (WMAP7 and SDSS DR7). We find that the decay vacuum model can describe the expansion rate at late times as well as the standard cosmological constant model but it fails to simultaneously reproduce the observed CMB and matter power spectrum. Its generalization $\barρ_Λ=3M_p^2(ξ_1 H_0 H+ξ_2 H^2)$ is also discussed. Detailed analysis of the background evolution shows that the dimensionless parameter $ξ_{2}$ would be zero to avoid the unnatural 'fine tuning' and to keep the positivity of energy density of dark matter and dark energy in the early epoch.

preprint2011arXiv

Combined constraints on modified Chaplygin gas model from cosmological observed data: Markov Chain Monte Carlo approach

We use the Markov Chain Monte Carlo method to investigate a global constraints on the modified Chaplygin gas (MCG) model as the unification of dark matter and dark energy from the latest observational data: the Union2 dataset of type supernovae Ia (SNIa), the observational Hubble data (OHD), the cluster X-ray gas mass fraction, the baryon acoustic oscillation (BAO), and the cosmic microwave background (CMB) data. In a flat universe, the constraint results for MCG model are, $Ω_{b}h^{2}=0.02263^{+0.00184}_{-0.00162}$ ($1σ$) $^{+0.00213}_{-0.00195}$ $(2σ)$, $B_{s}=0.7788^{+0.0736}_{-0.0723}$ ($1σ$) $^{+0.0918}_{-0.0904}$ $(2σ)$, $α=0.1079^{+0.3397}_{-0.2539}$ ($1σ$) $^{+0.4678}_{-0.2911}$ $(2σ)$, $B=0.00189^{+0.00583}_{-0.00756}$ ($1σ$) $^{+0.00660}_{-0.00915}$ $(2σ)$, and $H_{0}=70.711^{+4.188}_{-3.142}$ ($1σ$) $^{+5.281}_{-4.149}$ $(2σ)$.

preprint2011arXiv

Constraints on kinematic models from the latest observational data

Kinematical models are constrained by the latest observational data from geometry-distance measurements, which include 557 type Ia supernovae (SNIa) Union2 data and 15 observational Hubble data. Considering two parameterized deceleration parameter, the values of current deceleration parameter $q_{0}$, jerk parameter $j_{0}$ and transition redshift $z_{T}$, are obtained. Furthermore, we show the departures for two parameterized kinematical models from $Λ$CDM model according to the evolutions of jerk parameter $j(z)$. Also, it is shown that the constraint on jerk parameter $j(z)$ is weak by the current geometrical observed data.

preprint2011arXiv

Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach

We investigate observational constraints on the generalized Chaplygin gas (GCG) model including the gamma-ray bursts (GRBs) at high redshift obtained directly from the Union2 type Ia supernovae (SNe Ia) set. By using the Markov Chain Monte Carlo method, we constrain the GCG model with the cosmology-independent GRBs, as well as the Union2 set, the cosmic microwave background (CMB) observation from the Wilkinson Microwave Anisotropy Probe (WMAP7) result, and the baryonic acoustic oscillation (BAO) observation from the spectroscopic Sloan Digital Sky Survey (SDSS) data release 7 (DR7) galaxy sample. The best-fit values of the GCG model parameters are $A_S$=$0.7475_{-0.0539}^{+0.0556}(1σ)_{-0.0816}^{+0.0794}(2σ)$, $α$=$-0.0256_{-0.1326}^{+0.1760}(1σ)_{-0.1907}^{+0.2730}(2σ)$, and the effective matter density $Ω_{m}=0.2629_{-0.0153}^{+0.0155}(1σ)_{-0.0223}^{+0.0236}(2σ)$, which are more stringent than the previous results for constraining on GCG model parameters.

preprint2011arXiv

Cosmography: Supernovae Union2, Baryon Acoustic Oscillation, Observational Hubble Data and Gamma Ray Bursts

In this paper, a parametrization describing the kinematical state of the universe via cosmographic approach is considered, where the minimum input is the assumption of the cosmological principle, i.e. the Friedmann-Robertson-Walker metric. A distinguished feature is that the result does not depend on any gravity theory and dark energy models. As a result, a series of cosmographic parameters (deceleration parameter $q_0$, jerk parameter $j_0$ and snap parameter $s_0$) are constrained from the cosmic observations which include type Ia supernovae (SN) Union2, the Baryon Acoustic Oscillation (BAO), the observational Hubble data (OHD), the high redshift Gamma ray bursts (GRBs). By using Markov Chain Monte Carlo (MCMC) method, we find the best fit values of cosmographic parameters in $1σ$ regions: $H_0=74.299^{+4.932}_{-4.287}$, $q_0=-0.386^{+0.655}_{-0.618}$, $j_0=-4.925^{+6.658}_{-7.297}$ and $s_0=-26.404^{+20.964}_{-9.097}$ which are improved remarkably. The values of $q_0$ and $j_0$ are consistent with flat $Λ$CDM model in $1σ$ region. But the value of $s_0$ of flat $Λ$CDM model will go beyond the $1σ$ region.

preprint2011arXiv

Does accelerating universe indicates Brans-Dicke theory

The evolution of universe in Brans-Dicke (BD) theory is discussed in this paper. Considering a parameterized scenario for BD scalar field $ϕ=ϕ_{0}a^α$ which plays the role of gravitational "constant" $G$, we apply the Markov Chain Monte Carlo method to investigate a global constraints on BD theory with a self-interacting potential according to the current observational data: Union2 dataset of type supernovae Ia (SNIa), high-redshift Gamma-Ray Bursts (GRBs) data, observational Hubble data (OHD), the cluster X-ray gas mass fraction, the baryon acoustic oscillation (BAO), and the cosmic microwave background (CMB) data. It is shown that an expanded universe from deceleration to acceleration is given in this theory, and the constraint results of dimensionless matter density $Ω_{0m}$ and parameter $α$ are, $Ω_{0m}=0.286^{+0.037+0.050}_{-0.039-0.047}$ and $α=0.0046^{+0.0149+0.0171}_{-0.0171-0.0206}$ which is consistent with the result of current experiment exploration, $\midα\mid \leq 0.132124$. In addition, we use the geometrical diagnostic method, jerk parameter $j$, to distinguish the BD theory and cosmological constant model in Einstein's theory of general relativity.

preprint2011arXiv

Probing Ricci dark energy model with perturbations by using WMAP seven-year cosmic microwave background measurements, BAO and Type Ia supernovae

In this paper, we investigate the Ricci dark energy model with perturbations through the joint constraints of current cosmological data sets from dynamical and geometrical perspectives. We use the full cosmic microwave background information from WMAP seven-year data, the baryon acoustic oscillations from the Sloan Digital Sky Survey and the Two Degree Galaxy Redshift Survey, and type Ia supernovae from the Union2 compilation of the Supernova Cosmology Project Collaboration. A global constraint is performed by employing the Markov chain Monte Carlo method. With the best-fitting results, we show the differences of cosmic microwave background power spectra and background evolutions for the cosmological constant model and Ricci dark energy model with perturbations.

preprint2010arXiv

Area spectrum of near-extremal SdS black holes via the new interpretation of quasinormal modes

Motivated by the recent work about a new physical interpretation of quasinormal modes by Maggiore, we investigate the quantization of near-extremal Schwarzschild-de Sitter black holes in the four dimensional spacetime. Following Kunstatter's method, we derive the area and entropy spectrum of near-extremal Schwarzschild-de Sitter black holes which differs from Setare's result. Furthermore, we find that the derived a universal area spectrum is $2πn$ which is equally spaced.

preprint2010arXiv

Constraints on modified Chaplygin gas from recent observations and a comparison of its status with other models

In this Letter, a modified Chaplygin gas (MCG) model of unifying dark energy and dark matter with the exotic equation of state $p_{MCG}=Bρ_{MCG} -\frac A{ρ_{MCG}^α}$ is constrained from recently observed data: the 182 Gold SNe Ia, the 3-year WMAP and the SDSS baryon acoustic peak. It is shown that the best fit value of the three parameters ($B$,$B_{s}$,$α$) in MCG model are (-0.085,0.822,1.724). Furthermore, we find the best fit $w(z)$ crosses -1 in the past and the present best fit value $w(0)=-1.114<-1$, and the $1σ$ confidence level of $w(0)$ is $-0.946\leq w(0)\leq-1.282$. Finally, we find that the MCG model has the smallest $χ^{2}_{min}$ value in all eight given models. According to the Alaike Information Criterion (AIC) of model selection, we conclude that recent observational data support the MCG model as well as other popular models.

preprint2010arXiv

Cosmic Constraint to DGP Brane Model: Geometrical and Dynamical Perspectives

In this paper, the Dvali-Gabadadze-Porrati (DGP) brane model is confronted by current cosmic observational data sets from geometrical and dynamical perspectives. On the geometrical side, the recent released Union2 $557$ of type Ia supernovae (SN Ia), the baryon acoustic oscillation (BAO) from Sloan Digital Sky Survey and the Two Degree Galaxy Redshift Survey (transverse and radial to line-of-sight data points), the cosmic microwave background (CMB) measurement given by the seven-year Wilkinson Microwave Anisotropy Probe observations (shift parameters $R$, $l_a(z_\ast)$ and redshift at the last scatter surface $z_\ast$), ages of high redshifts galaxies, i.e. the lookback time (LT) and the high redshift Gamma Ray Bursts (GRBs) are used. On the dynamical side, data points about the growth function (GF) of matter linear perturbations are used. Using the same data sets combination, we also constrain the flat $Λ$CDM model as a comparison. The results show that current geometrical and dynamical observational data sets much favor flat $Λ$CDM model and the departure from it is above $4σ$($6σ$) for spatially flat DGP model with(without) SN systematic errors. The consistence of growth function data points is checked in terms of relative departure of redshift-distance relation.

preprint2010arXiv

Cosmological constraints on generalized Chaplygin gas model: Markov Chain Monte Carlo approach

We use the Markov Chain Monte Carlo method to investigate a global constraints on the generalized Chaplygin gas (GCG) model as the unification of dark matter and dark energy from the latest observational data: the Constitution dataset of type supernovae Ia (SNIa), the observational Hubble data (OHD), the cluster X-ray gas mass fraction, the baryon acoustic oscillation (BAO), and the cosmic microwave background (CMB) data. In a non-flat universe, the constraint results for GCG model are, $Ω_{b}h^{2}=0.0235^{+0.0021}_{-0.0018}$ ($1σ$) $^{+0.0028}_{-0.0022}$ $(2σ)$, $Ω_{k}=0.0035^{+0.0172}_{-0.0182}$ ($1σ$) $^{+0.0226}_{-0.0204}$ $(2σ)$, $A_{s}=0.753^{+0.037}_{-0.035}$ ($1σ$) $^{+0.045}_{-0.044}$ $(2σ)$, $α=0.043^{+0.102}_{-0.106}$ ($1σ$) $^{+0.134}_{-0.117}$ $(2σ)$, and $H_{0}=70.00^{+3.25}_{-2.92}$ ($1σ$) $^{+3.77}_{-3.67}$ $(2σ)$, which is more stringent than the previous results for constraint on GCG model parameters. Furthermore, according to the information criterion, it seems that the current observations much support $Λ$CDM model relative to the GCG model.

preprint2010arXiv

Current Observational Constraints to Holographic Dark Energy Model with New Infrared cut-off via Markov Chain Monte Carlo Method

In this paper, the holographic dark energy model with new infrared (IR) cut-off for both the flat case and the non-flat case are confronted with the combined constraints of current cosmological observations: type Ia Supernovae, Baryon Acoustic Oscillations, current Cosmic Microwave Background, and the observational hubble data. By utilizing the Markov Chain Monte Carlo (MCMC) method, we obtain the best fit values of the parameters with $1σ, 2σ$ errors in the flat model: $Ω_{b}h^2=0.0233^{+0.0009 +0.0013}_{-0.0009 -0.0014}$, $α=0.8502^{+0.0984 +0.1299}_{-0.0875 -0.1064}$, $β=0.4817^{+0.0842 +0.1176}_{-0.0773 -0.0955}$, $Ω_{de0}=0.7287^{+0.0296 +0.0432}_{-0.0294 -0.0429}$, $Ω_{m0}=0.2713^{+0.0294 +0.0429}_{-0.0296 -0.0432}$, $H_0=66.35^{+2.38 +3.35}_{-2.14 -3.07}$. In the non-flat model, the constraint results are found in $1σ, 2σ$ regions: $Ω_{b}h^2=0.0228^{+0.0010 +0.0014}_{-0.0010 -0.0014}$, $Ω_k=0.0305^{+0.0092 +0.0140}_{-0.0134 -0.0176}$, $α=0.8824^{+0.2180 +0.2213}_{-0.1163 -0.1378}$, $β=0.5016^{+0.0973 +0.1247}_{-0.0871 -0.1102}$, $Ω_{de0}=0.6934^{+0.0364 +0.0495}_{-0.0304 -0.0413}$, $Ω_{m0}=0.2762^{+0.0278 +0.0402}_{-0.0320 -0.0412}$, $H_0=70.20^{+3.03 +3.58}_{-3.17 -4.00}$. In the best fit holographic dark energy models, the equation of state of dark energy and the deceleration parameter at present are characterized by $w_{de0}=-1.1414\pm0.0608, q_0=-0.7476\pm0.0466$ (flat case) and $w_{de0}=-1.0653\pm0.0661, q_0=-0.6231\pm0.0569$ (non-flat case). Compared to the $Λ\textmd{CDM}$ model, it is found the current combined datasets do not favor the holographic dark energy model over the $Λ\textmd{CDM}$ model.

preprint2010arXiv

Geometrical Diagnostics for Generalized Chaplygin Gas

A new diagnostic method, $Om$ is applied to generalized Chaplygin gas (GCG) model as the unification of dark matter and dark energy. On the basis of the recently observed data: the Union supernovae, the observational Hubble data, the SDSS baryon acoustic peak and the five-year WMAP shift parameter, we show the discriminations between GCG and $Λ$CDM model. Furthermore, it is calculated that the current equation of state of dark energy $w_{0de}=-0.964$ according to GCG model.

preprint2010arXiv

Observational constraint on generalized Chaplygin gas model

We investigate observational constraints on the generalized Chaplygin gas (GCG) model as the unification of dark matter and dark energy from the latest observational data: the Union SNe Ia data, the observational Hubble data, the SDSS baryon acoustic peak and the five-year WMAP shift parameter. It is obtained that the best fit values of the GCG model parameters with their confidence level are $A_{s}=0.73^{+0.06}_{-0.06}$ ($1σ$) $^{+0.09}_{-0.09}$ $(2σ)$, $α=-0.09^{+0.15}_{-0.12}$ ($1σ$) $^{+0.26}_{-0.19}$ $(2σ)$. Furthermore in this model, we can see that the evolution of equation of state (EOS) for dark energy is similar to quiessence, and its current best-fit value is $w_{0de}=-0.96$ with the $1σ$ confidence level $-0.91\geq w_{0de}\geq-1.00$.

preprint2010arXiv

Observational constraints on holographic dark energy with varying gravitational constant

We use observational data from Type Ia Supernovae (SN), Baryon Acoustic Oscillations (BAO), Cosmic Microwave Background (CMB) and observational Hubble data (OHD), and the Markov Chain Monte Carlo (MCMC) method, to constrain the cosmological scenario of holographic dark energy with varying gravitational constant. We consider both flat and non-flat background geometry, and we present the corresponding constraints and contour-plots of the model parameters. We conclude that the scenario is compatible with observations. In 1$σ$ we find $Ω_{\Lambda0}=0.72^{+0.03}_{-0.03}$, $Ω_{k0}=-0.0013^{+0.0130}_{-0.0040}$, $c=0.80^{+0.19}_{-0.14}$ and $Δ_G\equiv G'/G=-0.0025^{+0.0080}_{-0.0050}$, while for the present value of the dark energy equation-of-state parameter we obtain $w_0=-1.04^{+0.15}_{-0.20}$.

preprint2010arXiv

Observational Constraints to Ricci Dark Energy Model by Using: SN, BAO, OHD, fgas Data Sets

In this paper, we perform a global constraint on the Ricci dark energy model with both the flat case and the non-flat case, using the Markov Chain Monte Carlo (MCMC) method and the combined observational data from the cluster X-ray gas mass fraction, Supernovae of type Ia (397), baryon acoustic oscillations, current Cosmic Microwave Background, and the observational Hubble function. In the flat model, we obtain the best fit values of the parameters in $1σ, 2σ$ regions: $Ω_{m0}=0.2927^{+0.0420 +0.0542}_{-0.0323 -0.0388}$, $α=0.3823^{+0.0331 +0.0415}_{-0.0418 -0.0541}$, $Age/Gyr=13.48^{+0.13 +0.17}_{-0.16 -0.21}$, $H_0=69.09^{+2.56 +3.09}_{-2.37 -3.39}$. In the non-flat model, the best fit parameters are found in $1σ, 2σ$ regions:$Ω_{m0}=0.3003^{+0.0367 +0.0429}_{-0.0371 -0.0423}$, $α=0.3845^{+0.0386 +0.0521}_{-0.0474 -0.0523}$, $Ω_k=0.0240^{+0.0109 +0.0133}_{-0.0130 -0.0153}$, $Age/Gyr=12.54^{+0.51 +0.65}_{-0.37 -0.49}$, $H_0=72.89^{+3.31 +3.88}_{-3.05 -3.72}$. Compared to the constraint results in the $Λ\textmd{CDM}$ model by using the same datasets, it is shown that the current combined datasets prefer the $Λ\textmd{CDM}$ model to the Ricci dark energy model.

preprint2010arXiv

Reconstructing Dark Energy Potentials From Parameterized Deceleration Parameters

In this paper, the properties of dark energy are investigated according to the parameterized deceleration parameter $q(z)$, which is used to describe the extent of the accelerating expansion of the universe. The potential of dark energy $V(ϕ)$ and the cosmological parameters, such as the dimensionless energy density $Ω_ϕ$, $Ω_{m}$, and the state parameter $w_ϕ$, are connected to it. Concretely, by giving two kinds of parameterized deceleration parameters $q(z)=a+\frac{bz}{1+z}$ and $q(z)=1/2+\frac{az+b}{(1+z)^2}$, the evolution of these parameters and the reconstructed potentials $V(ϕ)$ are plotted and analyzed. It's found that the potentials run away with the evolution of universe.

preprint2010arXiv

Scattering of scalar perturbations with cosmological constant in low-energy and high-energy regimes

We study the absorption and scattering of massless scalar waves propagating in spherically symmetric spacetimes with dynamical cosmological constant both in low-energy and high-energy zones. In the former low-energy regime, we solve analytically the Regge-Wheeler wave equation and obtain an analytic absorption probability expression which varies with $M\sqrtΛ$, where $M$ is the central mass and $Λ$ is cosmological constant. The low-energy absorption probability, which is in the range of $[0, 0.986701]$, increases monotonically with increase in $Λ$. In the latter high-energy regime, the scalar particles adopt their geometric optics limit value. The trajectory equation with effective potential emerges and the analytic high-energy greybody factor, which is relevant with the area of classically accessible regime, also increases monotonically with increase in $Λ$, as long $Λ$ is less than or of the order of $10^4$. In this high-energy case, the null cosmological constant result reduces to the Schwarzschild value $27πr_g^2/4$.

preprint2010arXiv

Testing the Consistence of Gamma Ray Burst Data-set and Supernovae Union2

In this paper, we test the consistency of Gamma Ray Bursts (GRBs) Data-set and Supernovae Union2 (SNU2) via the so-called {\it multi-dimensional consistency test} under the assumption that $Λ$CDM model is a potentially correct cosmological model. We find that the probes are inconsistent with $1.456σ$ and $85.47%$ in terms of probability. With this observation, it is concluded that GRBs can be combined with SNU2 to constrain cosmological models.

preprint2010arXiv

The Integrated Sachs-Wolfe Effect in Time Varying Vacuum Model

The integrated Sachs-Wolfe (ISW) effect is an important implication for dark energy. In this paper, we have calculated the power spectrum of the ISW effect in the time varying vacuum cosmological model, where the model parameter $β=4.407$ is obtained by the observational constraint of the growth rate. It's found that the source of the ISW effect is not only affected by the different evolutions of the Hubble function $H(a)$ and the dimensionless matter density $Ω_m(a)$, but also by the different growth function $D_+(a)$, all of which are changed due to the presence of matter production term in the time varying vacuum model. However, the difference of the ISW effect in $Λ(t)\textmd{CDM}$ model and $Λ\textmd{CDM}$ model is lessened to a certain extent due to the integration from the time of last scattering to the present. It's implied that the observations of the galaxies with high redshift are required to distinguish the two models.

preprint2010arXiv

Time Variable Cosmological Constants from Cosmological Horizons

In this paper, motivated from the fact that a de Sitter cosmological boundary corresponds to a positive cosmological constant, we consider time variable cosmological constants, dubbed {\it horizon cosmological constants}. The horizon cosmological constants correspond to Hubble horizon, future event horizon and particle horizon are discussed respectively. When the Hubble horizon is taken as a cosmological length scale, the effective equation of state of horizon cosmological constant is quintessence-like. The values of model parameter $c$ will determine the current status of our universe. When particle horizon is taken as the cosmological length scale, non viable cosmological model can be obtained for the requirement of $Ω_Λ<1/3$ which conflicts with current comic observations. When the future event horizon is taken as the role of cosmological length scale, the forms of effective equation of state of horizon cosmological constants are the the same as the holographic ones. But, their evolutions are different because of the effective interaction with cold dark matter.

preprint2009arXiv

Cosmic Constraint on Ricci Dark Energy Model

In this paper, a holographic dark energy model, dubbed Ricci dark energy, is confronted with cosmological observational data from type Ia supernovae (SN Ia), baryon acoustic oscillations (BAO) and cosmic microwave background (CMB). By using maximum likelihood method, it is found out that Ricci dark energy model is a viable candidate of dark energy model with the best fit parameters: $Ω_{m0}=0.34\pm 0.04$, $α=0.38\pm 0.03$ with $1σ$ error. Here, $α$ is a dimensionless parameter related with Ricci dark energy $ρ_{R}$ and Ricci scalar $R$, i.e., $ρ_{R}\propto αR$.

preprint2009arXiv

Time Variable Cosmological Constant from Renormalization Group Equations

In this paper, a time variable cosmological constant (CC) from renormalization group equations (RGEs) is explored, where the renormalization scale $μ^2=R^{-2}_{CC}=Max(\dot{H}+2H^2,-\dot{H})$ is taken. The cosmological parameters, such as dimensionless energy density, deceleration parameter and effective equation of state of CC etc, are derived. Also, the cosmic observational constraints are implemented to test the model's consistence. The results show that it is compatible with cosmic data. So, it would be a viable dark energy model.

preprint2009arXiv

Time Variable Cosmological Constants from the Age of Universe

In this paper, time variable cosmological constant, dubbed {\it age cosmological constant}, is investigated motivated by the fact: any cosmological length scale and time scale can introduce a cosmological constant or vacuum energy density into Einstein's theory. The age cosmological constant takes the form $ρ_Λ=3c^2M^2_P/t_Λ^2$, where $t_Λ$ is the age of our universe or conformal time. The effective equation of state of age cosmological constant are $w^{eff}_Λ=-1+{2/3}\frac{\sqrt{Ω_Λ}}{c}$ and $w^{eff}_Λ=-1+{2/3}\frac{\sqrt{Ω_Λ}}{c}(1+z)$ when the age of universe and conformal time are taken as the role of cosmological time scales respectively. They are the same as the so-called agegraphic dark energy models. However, the evolution history are different from the agegraphic ones for their different evolution equations.

preprint2008arXiv

Constraints on accelerating universe using ESSENCE and Gold supernovae data combined with other cosmological probes

We use recently observed data: the 192 ESSENCE type Ia supernovae (SNe Ia), the 182 Gold SNe Ia, the 3-year WMAP, the SDSS baryon acoustic peak, the X-ray gas mass fraction in clusters and the observational $H(z)$ data to constrain models of the accelerating universe. Combining the 192 ESSENCE data with the observational $H(z)$ data to constrain a parameterized deceleration parameter, we obtain the best fit values of transition redshift and current deceleration parameter $z_{T}=0.632^{+0.256}_{-0.127}$, $q_{0}=-0.788^{+0.182}_{-0.182}$. Furthermore, using $Λ$CDM model and two model-independent equation of state of dark energy, we find that the combined constraint from the 192 ESSENCE data and other four cosmological observations gives smaller values of $Ω_{0m}$ and $q_{0}$, but a larger value of $z_{T}$ than the combined constraint from the 182 Gold data with other four observations. Finally, according to the Akaike information criterion it is shown that the recently observed data equally supports three dark energy models: $Λ$CDM, $w_{de}(z)=w_{0}$ and $w_{de}(z)=w_{0}+w_{1}\ln(1+z)$.

preprint2007arXiv

Statefinder Parameters for Interacting Phantom Energy with Dark Matter

We apply in this paper the statefinder parameters to the interacting phantom energy with dark matter. There are two kinds of scaling solutions in this model. It is found that the evolving trajectories of these two scaling solutions in the statefinder parameter plane are quite different, and that are also different from the statefinder diagnostic of other dark energy models.

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external id: arxiv:2601.00256:author:1:lixin-xu

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external id: arxiv:2605.13838:author:2:lixin-xu

Imported May 20, 2026Synced May 21, 2026

17 works

Jianbo Lu

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Jianbo Lu contributes to research discovery and scholarly infrastructure.

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Yuting Wang

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Yuting Wang contributes to research discovery and scholarly infrastructure.

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Weiqiang Yang

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Weiqiang Yang contributes to research discovery and scholarly infrastructure.

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Baorong Chang

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Baorong Chang contributes to research discovery and scholarly infrastructure.

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Lixin Xu

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78 published item(s)

Equivariant Cohomology, BRST Quantization, and Analytic Localization: A Unified Framework

R-DMesh: Video-Guided 3D Animation via Rectified Dynamic Mesh Flow

Can phantom transition at $z\sim 1$ restore the Cosmic concordance?

Comparing the scalar-field dark energy models with recent observations

Limit on the dark matter mass from its interaction with photons

Testing the effect of $H_0$ on $fσ_8$ tension using a Gaussian Process method

General Cosmography Model with Spatial Curvature

Detecting the Neutrinos Mass Hierarchy from Cosmological Data

Distinguish three time-dependent dark energy models using statefinder pairs with error bars and Bayesian evidence

New constraints on cosmic polarization rotation from the ACTPol cosmic microwave background B-Mode polarization observation and the BICEP2 constraint update

Probing the Neutrino Mass through the Cross Correlation between the Rees-Sciama Effect and Weak Lensing

Thermodynamics of Apparent Horizon and Friedmann Equations in Big Bounce Universe

Constraint on $f(R)$ Gravity through the Redshift Space Distortion

Constraints on the dark matter equation of state with redshift-space distortion

Exploring a new interaction between dark matter and dark energy using the growth rate of structure

FRCAMB: An $f(R)$ Code for Anisotropies in the Microwave Background

Galaxy clustering, CMB and supernova data constraints on $ϕ$CDM model with massive neutrinos

Gravitational Waves: A Test for Modified Gravity

Reduced modified Chaplygin gas cosmology

Confronting Dark Energy Anisotropic Stress

Confronting DGP Braneworld Gravity with Cosmic Observations after Planck Data

Constraints on a decomposed dark fluid with constant adiabatic sound speed by jointing the geometry test and growth rate after Planck data

Cosmological constraints on interacting dark energy with redshift-space distortion after Planck data

Cosmology with hybrid expansion law: scalar field reconstruction of cosmic history and observational constraints

Coupled dark energy with perturbed Hubble expansion rate

Detecting Primordial Gravitational Waves Signal from BICEP2 and {\it Planck} HFI $353$GHz Dust Polarization

Interacting parametrized post-Friedmann method

Observational constraints on variable equation of state parameters of dark matter and dark energy after Planck

Post-$Planck$ constraints on interacting vacuum energy

Probing kinematics and fate of the Universe with linearly time-varying deceleration parameter

Pursuing the Amplitude of Tensor Mode Power Spectrum in Light of BICEP2

Reconciling the Tension Between Planck and BICEP2 Through Early Dark Energy

Spherical Collapse for Viscous Generalized Chaplygin Gas Model

Spherical top-hat Collapse of a Viscous Unified Dark Fluid

Testing coupled dark energy with large scale structure observation

Viscous Generalized Chaplygin Gas as a Unified Dark Fluid: Including Perturbation of Bulk Viscosity

Constraints on Dark Matter annihilation and Its Equation of State after Planck Data

Constraints on the Holographic Dark Energy Model from Type Ia Supernovae, WMAP7, Baryon Acoustic Oscillation and Redshift-Space Distortion

Cosmological constraints on a decomposed Chaplygin gas

Growth Index after the Planck Results

Spherical Collapse of a Unified Dark Fluid with Constant Adiabatic Sound Speed

Strong Gravitational Lensing and Its Cosmic Constraints

Unified Dark Fluid with Constant Adiabatic Sound Speed: Including Entropic Perturbations

Unified dark fluid with fast transition: including entropic perturbations

A New Unified Dark Fluid Model and Its Cosmic Constraint

Constraints to Holographic Dark Energy Model via Type Ia Supernovae, Baryon Acoustic Oscillation and WMAP

Cosmological Model-independent Gamma-ray Bursts Calibration and its Cosmological Constraint to Dark Energy

Modified Chaplygin Gas as a Unified Dark Matter and Dark Energy Model and Cosmic Constraints

Revisiting Cardassian Model and Cosmic Constraint

Revisiting Generalized Chaplygin Gas as a Unified Dark Matter and Dark Energy Model

Unified Dark Fluid with Constant Adiabatic Sound Speed and Cosmic Constraints

$Λ(t)$CDM Model as a Unified Origin of Holographic and Agegraphic Dark Energy Models

CMB Temperature and Matter Power Spectrum in a Decay Vacuum Dark Energy Model

Combined constraints on modified Chaplygin gas model from cosmological observed data: Markov Chain Monte Carlo approach

Constraints on kinematic models from the latest observational data

Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach

Cosmography: Supernovae Union2, Baryon Acoustic Oscillation, Observational Hubble Data and Gamma Ray Bursts

Does accelerating universe indicates Brans-Dicke theory

Probing Ricci dark energy model with perturbations by using WMAP seven-year cosmic microwave background measurements, BAO and Type Ia supernovae

Area spectrum of near-extremal SdS black holes via the new interpretation of quasinormal modes

Constraints on modified Chaplygin gas from recent observations and a comparison of its status with other models

Cosmic Constraint to DGP Brane Model: Geometrical and Dynamical Perspectives

Cosmological constraints on generalized Chaplygin gas model: Markov Chain Monte Carlo approach

Current Observational Constraints to Holographic Dark Energy Model with New Infrared cut-off via Markov Chain Monte Carlo Method

Geometrical Diagnostics for Generalized Chaplygin Gas

Observational constraint on generalized Chaplygin gas model

Observational constraints on holographic dark energy with varying gravitational constant

Observational Constraints to Ricci Dark Energy Model by Using: SN, BAO, OHD, fgas Data Sets

Reconstructing Dark Energy Potentials From Parameterized Deceleration Parameters

Scattering of scalar perturbations with cosmological constant in low-energy and high-energy regimes

Testing the Consistence of Gamma Ray Burst Data-set and Supernovae Union2

The Integrated Sachs-Wolfe Effect in Time Varying Vacuum Model

Time Variable Cosmological Constants from Cosmological Horizons

Cosmic Constraint on Ricci Dark Energy Model